Details

analyze609.0ms (12.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.4s (50.2%)

Results

978.0ms	1336×	body	1024	valid
975.0ms	5910×	body	128	valid
273.0ms	674×	body	512	valid
92.0ms	332×	body	256	valid
5.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	22	12
3	26	12
4	26	12

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

Compiler

Compiled 44 to 25 computations (43.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 y)
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
✓	0.0b	(+.f64 x (sin.f64 y))
✓	0.1b	(*.f64 z (cos.f64 y))

series26.0ms (0.6%)

Counts

4 → 88

Calls

4 calls:

11.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
9.0ms	(*.f64 z (cos.f64 y))
4.0ms	(+.f64 x (sin.f64 y))
2.0ms	(cos.f64 y)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
11×	`add-log-exp_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`fma-def_binary64`

Counts

4 → 65

Calls

4 calls:

5.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
4.0ms	(*.f64 z (cos.f64 y))
2.0ms	(+.f64 x (sin.f64 y))
1.0ms	(cos.f64 y)

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1040×	`fma-neg_binary64`
502×	`fma-def_binary64`
391×	`associate-l_binary64`
327×	`associate-r_binary64`
287×	`distribute-rgt-neg-in_binary64`

Counts

153 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1501
1	363	1428
2	1043	1407
3	3441	1406
4	4620	1406
5	4985	1406

prune72.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Error

0.0b

Counts

125 → 4

Alt Table

Status	Error	Program
▶	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	31.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y)))))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	18.3b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))

Compiler

Compiled 1935 to 599 computations (69% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 z) (cos.f64 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series250.0ms (5.3%)

Counts

4 → 72

Calls

4 calls:

159.0ms	(*.f64 (cbrt.f64 z) (cos.f64 y))
37.0ms	(cbrt.f64 z)
34.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
20.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y)))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
7.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y)))
3.0ms	(*.f64 (cbrt.f64 z) (cos.f64 y))
1.0ms	(cbrt.f64 z)

simplify139.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
458×	`*-commutative_binary64`
421×	`cancel-sign-sub-inv_binary64`
385×	`unswap-sqr_binary64`
323×	`sub-neg_binary64`

Counts

175 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1636
1	297	1460
2	1128	1401
3	2242	1385
4	4280	1287
5	4570	1287
6	4884	1287
7	4872	1287

prune115.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	185	6	191

Error

0.0b

Counts

191 → 6

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	31.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y)))))
▶	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))))
	2.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	18.3b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))

Compiler

Compiled 4029 to 1061 computations (73.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.6b	(cbrt.f64 z)

series184.0ms (3.9%)

Counts

2 → 36

Calls

2 calls:

162.0ms	(cbrt.f64 (cos.f64 y))
22.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
34×	`pow1_binary64`
29×	`pow-prod-down_binary64`
24×	`cbrt-unprod_binary64`
24×	`prod-exp_binary64`

Counts

2 → 50

Calls

2 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
1.0ms	(cbrt.f64 (cos.f64 y))

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

644×	`fma-def_binary64`
636×	`fma-neg_binary64`
411×	`unswap-sqr_binary64`
385×	`*-commutative_binary64`
245×	`associate-+l+_binary64`

Counts

86 → 71

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	113	1041
1	274	682
2	885	670
3	1882	662
4	4515	660
5	4973	660

prune176.0ms (3.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	227	6	233

Error

0.0b

Counts

233 → 6

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	31.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y)))))
✓	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))))
▶	2.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	18.3b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))

Compiler

Compiled 6803 to 1407 computations (79.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (cos.f64 y)))
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.6b	(cbrt.f64 z)
✓	2.5b	(expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series56.0ms (1.2%)

Counts

2 → 36

Calls

2 calls:

37.0ms	(expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
19.0ms	(.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (cos.f64 y)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`add-cbrt-cube_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

2 → 31

Calls

2 calls:

4.0ms	(.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (cos.f64 y)))
0.0ms	(expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

simplify80.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-l_binary64`
509×	`fma-def_binary64`
428×	`cancel-sign-sub-inv_binary64`
413×	`associate-r_binary64`
383×	`unswap-sqr_binary64`

Counts

67 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	881
1	171	562
2	490	536
3	1536	530
4	4083	530
5	4640	530
6	4955	530

prune128.0ms (2.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	169	6	175

Error

0.0b

Counts

175 → 6

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	31.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (*.f64 z (cos.f64 y)))))
✓	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))))
✓	2.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	18.3b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))

Compiler

Compiled 3803 to 1041 computations (72.6% saved)

regimes142.0ms (3%)

Accuracy

Total 0.0b remaining (43.2%)

Threshold costs 0.0b (43.2%)

Counts

35 → 1

Compiler

Compiled 2244 to 1426 computations (36.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end86.0ms (1.8%)

Compiler: Compiled 138 to 80 computations (42% saved)

Details

analyze609.0ms (12.9%)

sample2.4s (50.2%)

simplify6.0ms (0.1%)

prune7.0ms (0.1%)

localize8.0ms (0.2%)

series26.0ms (0.6%)

rewrite14.0ms (0.3%)

simplify89.0ms (1.9%)

prune72.0ms (1.5%)

localize11.0ms (0.2%)

series250.0ms (5.3%)

rewrite24.0ms (0.5%)

simplify139.0ms (2.9%)

prune115.0ms (2.4%)

localize14.0ms (0.3%)

series184.0ms (3.9%)

rewrite22.0ms (0.5%)

simplify69.0ms (1.5%)

prune176.0ms (3.7%)

localize13.0ms (0.3%)

series56.0ms (1.2%)

rewrite6.0ms (0.1%)

simplify80.0ms (1.7%)

prune128.0ms (2.7%)

regimes142.0ms (3%)

simplify3.0ms (0.1%)

end86.0ms (1.8%)

Profiling